Q. 24.6( 16 Votes )

# Find the dimensio

Answer :

A. Angular speed is the rate of change of angular position of an object w.r.t. time.

Dimensions of dθ =[M^{0}L^{0}T^{0}]

Dimensions of dt = [T]

Dimensions of ω = .

B. Angular acceleration is the rate of change of angular speed w.r.t time.

Dimensions of dω =

Dimensions of dt = [T]

Dimensions of =

C. Torque is the rotational effect of a linear force. It is the turning effect when a force is applied on a body that can rotate.

Torque(T) = Force(F) × distance from axis (r)

Dimensions of F = [MLT^{-2}]

Dimensions of r = [L^{1}]

Dimensions of T = [MLT^{-2}] × [L^{1}] = [ML^{2}T^{-2}]

D. Moment of inertia is defined as the inertia of a rotating body w.r.t. its axis of rotation.

Moment of inertia (I) = mass of body (m) × square of ⊥ distance from axis(r^{2})

Dimensions of m = [M]

Dimensions of r^{2} = [L^{2}]

Dimensions of I = [M] × [L^{2}] = [ML^{2}]

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